Combining pulleys on a lever

Question

Hi all, I hope this is an appropriate forum for this question. 

I am trying to design a cheese press and I want to make sure I am calculating the force properly. So the basic idea is a have a lever with a weight hanging on it and I want to control the amount of force applied at a certain place (on the same side of the fulcrum as the weight).  The place where the force needs to be calculated is 1 foot from the fulcrum and the place where the weight is to be applied is 4 feet from the fulcrum.  Ok so mechanical advantage of 4:1.  Now when I add in two pulleys like in the image below, I think that since the pulleys are stationary the pully system isn't changing my mechanical advantage.  However, now there are two places on the lever that a force is being applied.  One with a 4:1 mechanical advantage and the other with a 2:1.  Here is where I am uncertain.  The connection at the 2 foot mark has one tension applied while the connection at the 4 foot mark has two (one directly downward and one at an angle).  

To calculate the total force on my press do I need to calculate the force from both tensions at the 4 foot hook up point?

Answer 1

Assuming the usual massless pulleys and string, the tensions are all equal. When horizontal, the effective force at 4ft is T + T/sqrt(2), not 2T, because the string joining the two pulleys is at a 45 degree angle, so then the mechanical advantage is (6+2sqrt(2)):1, or about 8.8:1, assuming the lower pulley is at floor level. If the bottom pulley is 6 inches off the ground, the advantage drops to 8.4:1.

Do you want it for all angles of the press? The string between the attachment point at two feet and the bottom pulley will rub as the angle increases.

Comments

Shouldn't the tension of the rope at 2ft be added in as well?